50 The Spectroscope : (January, 
If the difference between b, and h, =6, that between c, and 
g, =6,, and that between d, and f, =8,, then the differences 
between each pair of 6,, 6,, and 6,, constitute an arithmetical 
progression. 
In all regular media there are two nodes, at which the 
sign of x changes from plus to minus, the one situated be- 
tween C and D, the other between F and G. Irregular 
media differ from regular in the position and number of these 
nodes, and in the arrangement of the quantities plus x and 
minus x; but the sums of each of these are always equal. 
These laws, and the mode of their application to the 
correction of the observed indices of refraction, may be illus- 
trated by a single example. For this purpose the specimen 
of flint glass marked No. 30 by Fraiinhofer may be seleCted. 
The indices of refraction, as determined by him, are as 
hayalere 
Be Cc D. Ey F, G. 1Ble 
1°623570, 1°625477, 1°630585, 1°637356, 1°643466, 1°655406, 1°666072. 
The normal wave-lengths corresponding to these seven 
lines, as observed by Angstrom, and corrected by the 
formulz according to which they are calculated from E, are 
as follows, E being assumed as unity, and the others stated 
in reference to that standard :— 
B. c: Det car he G. H. 
1°3033839, 1°245493, I°1189003, I, 0°922576, 0°8175183, 0°7464871. 
The lines D, E, and H, in the spectrum are double; but it 
is the less refrangible D, and the more refrangible E and H, 
whose wave-lengths are here given. 
The internal wave-lengths in flint glass, No. 30, are found 
by dividing each of the above normal wave-lengths by its 
corresponding index of refraction. This gives the following 
aes F—— 
b. Cs d. é. Fr g. h. 
0°802789, 0°766232, 0686196, 0°610741, 0°561360, 0°493848, 0°448052. 
The constants, < and a, for the formula 
U 
= Uy 
é 
are found thus :— 
-— (3B+2C+D)—(F+2G + 3H) 
(3b+2c+d)—(f+2g+ 3h) ’ 
and its value in this case is 1°570504. ‘Then, calling the 
